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i0_0_to_1_fast

pxfm::bessel::k0

Function i0_0_to_1_fast 

Source 
fn i0_0_to_1_fast(x: f64) -> DoubleDouble
Expand description

Computes I0 on interval [0; 1] as rational approximation I0 = 1 + (x/2)^2 * Pn((x/2)^2)/Qm((x/2)^2))

Generated by Wolfram Mathematica:

<<FunctionApproximations`
ClearAll["Global`*"]
f[x_]:=(BesselI[0,x]-1)/(x/2)^2
g[z_]:=f[2 Sqrt[z]]
{err,approx}=MiniMaxApproximation[g[z],{z,{0.0000000000001,1},5,5},WorkingPrecision->60]
poly=Numerator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]
poly=Denominator[approx][[1]];
coeffs=CoefficientList[poly,z];
TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50},ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]